A thick spherical shell occupies the region between two spheres of radii a and 2a, both centred on the origin. The shell is made of a material with Az² where A is a constant. density p= (a) Show that the density expressed in spherical coordinates (r, 0, 6) is p = Arcos² 0. (b) Hence, or otherwise, find the mass M of the shell by evaluating a suitable volume integral. (Hint: To evaluate the integral sin 0 cos² 0 do, use the substitution u = cos 0.)
A thick spherical shell occupies the region between two spheres of radii a and 2a, both centred on the origin. The shell is made of a material with Az² where A is a constant. density p= (a) Show that the density expressed in spherical coordinates (r, 0, 6) is p = Arcos² 0. (b) Hence, or otherwise, find the mass M of the shell by evaluating a suitable volume integral. (Hint: To evaluate the integral sin 0 cos² 0 do, use the substitution u = cos 0.)
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A thick spherical shell occupies the region between two spheres of radii a
and 2a, both centred on the origin. The shell is made of a material with
where A is a constant.
density p=
Az²
(a) Show that the density expressed in spherical coordinates (r, 0,6) is
p = Arcos² 0.
(b) Hence, or otherwise, find the mass M of the shell by evaluating a
suitable volume integral.
(Hint: To evaluate the integral
sin cos² 0 do,
use the substitution u = cos 0.)
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